Simplify the following expression: $\dfrac{132p^4}{33p}$ You can assume $p \neq 0$.
Solution: $ \dfrac{132p^4}{33p} = \dfrac{132}{33} \cdot \dfrac{p^4}{p} $ To simplify $\frac{132}{33}$ , find the greatest common factor (GCD) of $132$ and $33$ $132 = 2 \cdot 2 \cdot 3 \cdot 11$ $33 = 3 \cdot 11$ $ \mbox{GCD}(132, 33) = 3 \cdot 11 = 33 $ $ \dfrac{132}{33} \cdot \dfrac{p^4}{p} = \dfrac{33 \cdot 4}{33 \cdot 1} \cdot \dfrac{p^4}{p} $ $\phantom{ \dfrac{132}{33} \cdot \dfrac{4}{1}} = 4 \cdot \dfrac{p^4}{p} $ $ \dfrac{p^4}{p} = \dfrac{p \cdot p \cdot p \cdot p}{p} = p^3 $ $ 4 \cdot p^3 = 4p^3 $